We propose and analyze the detector of modulated terahertz (THz) radiation based on the graphene field-effect transistor with mechanically floating gate made of graphene as well. The THz component of incoming radiation induces resonant excitation of plasma oscillations in graphene layers (GLs). The rectified component of the ponderomotive force between GLs invokes resonant mechanical swinging of top GL, resulting in the drain current oscillations. To estimate the device responsivity, we solve the hydrodynamic equations for the electrons and holes in graphene governing the plasma-wave response, and the equation describing the graphene membrane oscillations. The combined plasma-mechanical resonance raises the current amplitude by up to four orders of magnitude. The use of graphene as a material for the elastic gate and conductive channel allows the voltage tuning of both resonant frequencies in a wide range.
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